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Research Summary: To engineer semiconductor nanosystems where interactions can be controlled and studied. Systems of interest are quantum wires, quantum wells, and quantum Hall effect. The quantum numbers to be manipulated are the spin index, valley index, and layer index in multilayer systems, measured at low temperatures and high magnetic fields where Luttinger liquids, quantum Hall ferromagnets, and multi-valley systems can be probed. This research will have applications in quantum information processing and cryogenic thermoelectrics